I have allergies and I have to wear a dust mask when house cleaning to prevent sore throat, sinus problems and the like, so I would say yes, dust can aggravate your throat.

Wind? That always gets me in the ears and throat, especially in winter. I get the sensation after I have been in the wind that my uvula is swollen and it is hard to swallow. Throat lozenges and sipping a lot of water seems to help.